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Nuclear Rings in Galaxies—A Kinematic Perspective

Lisa. M. MazzucaNASA Goddard Space Flight Center, Mission Validation and Operations Branch (Code 584), Greenbelt,

MD 20771, USA

Robert A. SwatersDepartment of Astronomy, University of Maryland, College Park MD 20742, USA

Johan H. KnapenInstituto de Astrofısica de Canarias, E-38200 La Laguna, Spain and

Departamento de Astrofısica, Universidad de La Laguna, E-38205 La Laguna,Spain

Sylvain VeilleuxDepartment of Astronomy, University of Maryland, College Park MD 20742, USA

ABSTRACT

We combine DensePak integral field unit and TAURUS Fabry-Perot observations of 13 nuclearrings to show an interconnection between the kinematic properties of the rings and their resonantorigin. The nuclear rings have regular and symmetric kinematics, and lack strong non-circularmotions. This symmetry, coupled with a direct relationship between the position angles andellipticities of the rings and those of their host galaxies, indicate the rings are in the same planeas the disc and are circular. From the rotation curves derived, we have estimated the compactness(v2/r) up to the turnover radius, which is where the nuclear rings reside. We find that there isevidence of a correlation between compactness and ring width and size. Radially wide rings areless compact, and thus have lower mass concentration. The compactness increases as the ringwidth decreases. We also find that the nuclear ring size is dependent on the bar strength, withweaker bars allowing rings of any size to form.

Subject headings: Galaxies: kinematics and dynamics - galaxies: spiral - galaxies: structure - galaxies:nuclei

1. Introduction

Nuclear rings in the central kiloparsecs ofgalaxies are usually observed as conglomera-tions of young massive stars in distinct compactgroupings (Buta & Combes 1996; Knapen 2005;Comeron et al. 2010). The star forming ringsare believed to form as a result of radial gas in-flow towards the central region, which stagnatesnear dynamical resonances. In barred galaxiesthe inflow originates in the gravitational torquesset up by the bar (e.g., Athanassoula (1992);

Heller & Shlosman (1994, 1996); Piner et al.(1995); Knapen et al. (1995); Buta & Combes(1996); Regan et al. (1997); Benedict et al. (2002)).Some 20% of nuclear rings occur in non-barredgalaxies (Knapen 2005; Comeron et al. 2010) andin those cases the inflow and resonances may wellbe related to the presence of weak ovals, past in-teractions or mergers, or even strong spiral arms.A resonant origin of all nuclear rings is most plau-sible.

The radial location of a nuclear ring can be

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described by the position of the inner Lind-blad resonance(s) (ILRs) (Simkin et al. 1980;Shlosman et al. 1989; Buta & Crocker 1993; Friedli & Benz1993; Heller & Shlosman 1994; Knapen et al.1995; Buta & Combes 1996), which is typi-cally at ∼1 kpc from the galaxy center al-though smaller and larger nuclear rings exist(Buta & Crocker 1993; Comeron et al. 2010). Ina non-axisymmetric potential, the nuclear ringforms near the ILR(s), where the inflowing molec-ular gas slows down, accumulates, and initiatesstar formation. For barred spiral galaxies, thering can be formed inside the large scale galacticspiral structure in the vicinity of the inner Lind-blad resonances (ILRs), which occur at those radiiwhere the bar pattern speed Ωb equals (Ω− κ/2),with Ω the angular velocity and kappa the ra-dial epicyclic frequency. This approximation isnot valid for strong bars where a non-linear anal-ysis must be performed, but in any case servesas a useful indication of how the location of thering is related to the underlying galaxy dynamics(Knapen et al. 1995).

Only a few in-depth observational studies of thekinematics of nuclear rings at high angular res-olution exist, but these have revealed some con-sistent kinematic characteristics of nuclear rings.Benedict et al. (1996) showed that non-circularmotions near the intersection of the ring andbar dust lanes correspond to radially inflowingmolecular gas that is apparently feeding the ringin NGC 4314. Reynaud & Downes (1998) con-cluded for NGC 1530 the existence of weak ve-locity transitions at the ends of the bar whichare inversely correlated with strong star forma-tion in the same areas, including the nuclear ringlocation. Regan et al. (1997) further note an in-crease in the residual velocity along an axis per-pendicular to the bar. Knapen et al. (2000) (seealso Knapen et al. (1995)) and Zurita et al. (2004)used CO and Hα emission in the central region ofNGC 4321 and NGC 1530, respectively, to revealgas streaming inward towards the ring along thebar dust lanes. Jogee et al. (2002) studied the fu-eling mechanisms of the ring in NGC 5248 to de-duce that large star forming clusters in the ringhave been triggered by a bar-driven spiral densitywave. More recently, Allard et al. (2006) followup on the ring in NGC 4321 to show relativelylow Hβ gas dispersion within the ring, which can

be an indicator of active star formation and coolgas inflow from which the massive stars inheritedthe low velocity dispersion.

The existing kinematic studies provide insightinto a small number of nuclear rings, but fail toreach more general conclusions applicable to theoverall population. Apart from the differing char-acteristics of the data used in these studies, this isdue mostly to the intrinsically small angular sizeof nuclear rings, and the dusty environments inwhich they exist, both of which make rings non-trivial to observe with most common instrumentsyielding kinematic data. In this paper we endeavorto start rectifying this situation by presenting amore homogeneous data set on thirteen nuclearrings.

The nuclear rings studied spectroscopically inthe current paper were all part of the sample ofMazzuca et al. (2008) (hereafter known as M08),who provided photometric insight into the strongstar forming nature of nuclear rings. From theirHα observational study of 22 nuclear rings, theyfind that many of the rings exhibit a well-definedage distribution pattern. M08 conclude that thisoccurrence can be a result of the combination ofbar-induced dynamics and gravitational instabil-ities which are occurring in the proximity of therings. These results add credence to the idea thatthe mass inflow driven by the bar along the dustlanes to the ring contact points is a key require-ment for the fueling of active (i.e., star forming)nuclear rings (and might also yield a possible sig-nature in the form of non-circular motions). Fur-ther evidence for this idea from detailed observa-tions of a handful of galaxies has been presentedby, e.g., Allard et al. (2006); Boker et al. (2008),and Knapen et al. (2010).

We now use kinematic information within andjust outside the nuclear rings in 13 galaxies to in-vestigate the possible relations between the opticalmorphology of the rings, the parameters derivedfrom the rotation curve, and their resonant na-ture. We begin by presenting an overview of theobservations and morphological properties of theHα sample in Section 2. We discuss the basic datareduction method, which includes the construc-tion of the velocity field maps, in Section 3. InSection 4 we discuss the kinematic parameters as-sociated with the ring rotation curves, and presentresults pertaining to non-circular motions in and

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around the nuclear rings, including velocity resid-uals. Our detailed analysis of the results is dis-cussed in Section 5, with concluding remarks inSection 6.

2. Sample and Observations

The galaxies studied here (see Table 1) forma subset of the sample presented in the imagingsurvey of M08 (which was based on B, I, andHα imaging). The data in M08 were obtained tocharacterize the morphology of the nuclear rings,and to analyze the age distribution of the indi-vidual stellar clusters forming each ring using theHα equivalent width. Results from this photo-metrically based survey reveal that the rings con-tain very young (1 Myr to 10 Myrs) hot massivestars, with some of the youngest clusters located inproximity to one or both of the intersection pointsof the bar dust lanes and the outer edge of thering. The ring ellipticity and position angle ap-proximately match that of the respective galac-tic disk, indicating that the rings are in the sameplane as the disk and are circular (M08; see alsoComeron et al. (2010)).

The kinematic sample was chosen from theimaging parent sample based on unambiguous de-tection of H ii regions delineating the ring, a non-zero inclination (i), and a measurable ring posi-tion angle (φr). Rings too diffuse or small, orwith no resolved H ii regions detected using themethod described in M08 (i.e., weak signal andresolution), were rejected. With the Densepak in-strument we cannot detect any H ii regions fornuclear rings with angular sizes less than 0.′′5 inradius, however, we have previously unpublishedhigh resolution Fabry-Perot Hα data of NGC 1300and NGC 6951 from the TAURUS instrument onthe 4.2m William Herschel Telescope, which weinclude in this sample. Similarly, we have usedthe TAURUS data for NGC 4321 from Knapenet al. (2000), a nuclear ring which meets our cri-teria but was added to the M08 sample after theDensePak observing runs. Lastly, although not in-cluded in the M08 sample, we observed two wellknown nuclear rings (NGC 2903 and NGC 3351)during the December 2003 run, which we also addto this sample.

We obtained two-dimensional Hα velocity fieldsof the sample over two observing runs, in De-

cember 2003 and April 2004, using the DensePak

fiber-optic array and bench spectrograph on the3.5m WIYN1 telescope. The DensePak integralfield unit (IFU) spectrograph (Barden & Wade1988) consists of 91 fibers bonded into a 7 × 13staggered rectangular grid that covers an area of30 × 45 arcsec of sky with center-to-center fiber(each fiber is 2.82 arcsec in diameter) spacings of3.75 arcsec. Four of the fibers are allocated as skyfibers, and are spaced around the grid roughly 1′

from the center. The spectrograph was configuredwith the Bench camera, which uses a Tek 2048CCD (T2KC), with the 860 lmm−1 grating, inthe second order, centered at 6575 A. We used athird order blocking filter (GG495). This arr ange-ment provided a final spectral coverage of 925 A,from 6085 A to 7010 A, at a resolution of 0.45 A perpixel. The spectral range included Hα as well asthe [N ii]λλ6548, 6583 and [S ii]λλ6716, 6731 lines.The effective instrumental resolution was differentfor the two runs, which is likely due to differencesin the instrument setup. For the December 2003run, the instrumental resolution (FWHM) aver-aged 0.97 A (44 kms−1) around Hα, with the res-olution for the April 2004 run 1.31 A (60 km s−1).

The array contains six dead fibers which de-creases the number of active fibers to 85. To avoidthese areas, the projected image of each nuclearring was placed in the upper half of the fiber ar-ray. Because of this method, many of the ringswere close to the edge of the field of view (FOV)along the array minor axis, which limits our dis-cussion of the environment exterior to the rings.We used two to four pointings, each of 1800 s induration, offset to fill the area of the dead fibers.This method also improved the sampling in somecases. For all exposures, the major axis of thearray was aligned along a North-South direction.

The Fabry-Perot observations for NGC 4321 aredetailed in Knapen et al. (2000), with very sim-ilar procedures implemented for NGC 1300 andNGC 6951. The pixel size in the reduced Fabry-Perot cubes is 0.27 arcsec squared, and the sep-aration between velocity channels is 15.7 km s−1.Each cube has 55 planes, thus covering a total ve-locity range of just over 1000 km s−1. Continuum

1Joint facility of the University of Wisconsin-Madison, Indi-ana University, Yale University, and National Optical As-tronomy Observatories

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Table 1: Morphological and photometric parameters of DensePak sampleNGC Morph Offset i φr φd φb ǫr ǫd Radius Radius Run

Type x y Date(′′) (′′) () () () () (′′) (kpc)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)473 SAB(r)0/a −4.4 +7.2 49 154 153 164 0.37 0.37 12.2 × 6.9 1.7 × 1.0 Dec031300 SB(rs)b n/a n/a 40 135 106 102 0.25 0.34 4.1 x 3.1 0.3 x 0.2 Sep981343 SAB(s)b −4.4 +7.8 41 60 80 82 0.25 0.37 8.8 × 6.6 1.2 × 0.9 Dec031530 SB(rs)b −1.6 +11.3 48 25 8 122 0.35 0.29 6.8 × 4.9 1.2 × 0.8 Dec032903 SAB(rs)bc −6.8 +8.3 65 8 17 24 0.4 0.52 1.7 × 1.0 0.06 × 0.04 Dec033351 SB(r)b −4.2 +6.1 34 20 13 112 0.3 0.32 2.7 × 1.9 0.15 × 0.11 Dec034303 SAB(rs)bc −3.3 +7.5 18 88 − 10 0.14 0.11 3.3 × 2.8 0.2 × 0.2 Apr044314 SB(rs)a −3.0 +6.3 26 135 − 135 0.1 0.11 6.6 × 5.9 0.3 × 0.3 Apr044321 SAB(s)bc n/a n/a 30 170 30 153 0.12 0.15 8.8 x 7.0 0.7 x 0.6 May955248 SAB(rs)bc −3.3 +6.5 46 115 110 137 0.3 0.28 6.6 × 4.6 0.7 × 0.5 Apr045953 SAa −6.0 +6.6 26 172 169 no bar 0.1 0.17 6.1 × 5.5 1.0 × 0.9 Apr046951 SAB(rs)bc n/a n/a 45 146 170 85 0.2 0.17 4.6 x 3.7 0.5 x 0.4 Sep937742 SA(r)b +0.7 +7.5 18 133 − no bar 0.05 0 9.9 × 9.4 1.0 × 1.0 Dec03

Notes: Morphological and photometric parameters for the observed sample. Galaxies are listed by NGCnumber in order of increasing RA (col. 1) with morphological type (col. 2) from de Vaucouleurs et al. (1991;hereafter RC3). Col. 3 lists the offset of the optical center of the Hα image from the center of the DensePakarray; this is not applicable to the TAURUS data for NGC 1300, NGC 4321, and NGC 6951. The nuclearring inclination i (col. 4) and photometric ring position angle φr (col. 5) have been derived from Hα imagingby M08). The disk position angle φd (col. 6) is from the RC3 with a dash indicating that a ring is circularwith no definable position angle. The bar position angle φb (col. 7) and photometric ring ellipticity ǫr (col. 8)are from M08. Disk ellipticity ǫd (col. 9) is from RC3. The radius of the ring, shown as the semi-major axisby the semi-minor axis (col. 10 and col. 11), was derived from the imaging data of M08 using the distancegiven there. The ring semi-major axis and ring ellipticity values are all consistent with those reported inComeron et al. (2010), taking into account that the methodology applied was slightly different. Run datesare in col. 12.

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subtraction was performed using the channels oneither extreme end of this range.

3. Data Reduction

The raw CCD frames of the DensePak datawere zero- and bias-corrected, flat-fielded, cosmic-ray cleaned, and combined using the standardiraf noao packages (zerocombine, ccdproc,

flatcombine, cosmicrays, and imcombine, re-spectively). The combined images were wavelength-calibrated using the noao iraf data reductionpackage dohydra to extract the spectrum yieldedby each fiber. A CuAr comparison source wasused for wavelength calibration. The reducedtwo-dimensional spectral image contains 89 rows(comprising 85 data fibers and 4 sky fibers), whereeach row is one pixel in height and corresponds toa single fiber.

We created gipsy2 scripts to identify and

then subtract the continuum and sky from thespectrum following the method described inBershady et al. (2005). Due to pointing uncer-tainties inherent to the instrument, we establishedthe measured pointing offsets (i.e., the shift fromthe center of the DensePak fiber array to the ringcenter) from the observations themselves. Wefollowed the procedure outlined in Swaters et al.(2003), in which the continuum levels measuredfrom the spectra are compared with levels derivedfrom a reference image with known coordinates.For our sample we used the I-band images fromM08. By repeating this process for all positionsnear the nominal pointing, we created a grid ofχ2 values, in which the minimum χ2 correspondsto the measured pointing offset. We estimatethat the uncertainty on the derived pointing isapproximately 0.5 arcsec. Because the sky fiberscontained no Hα emission from the target galaxy,we used the average of the four reserved DensePak

sky fibers, each located 1 arcmin from the centerof the array.

To combine the pointings into a sparse velocityfield, we first fitted Gaussians to the continuum-and sky-subtracted Hα emission line profiles, usinga 3σ threshold to avoid spurious detections. Thefitted velocities derived for each fiber were placedin a map at corresponding fiber positions. The

2Groningen Image Processing System,http://www.astro.rug.nl/gipsy

observed radial velocities were corrected to helio-centric velocities. In the cases of multiple velocitymeasurements for the same pixel in the velocityfield, we averaged the measured velocities. To aidin the visual representation of the sparse velocityfield, we also constructed interpolated smoothedvelocity field maps. We replaced each data pointin the sparse velocity field with a Gaussian beamof 5.5 arcsec and weighted the overlapping sectionsbetween the points by the relative intensities of theoverlapping Gaussians. The resulting smoothedvelocity fields are shown in Figure 1 (left, panel 1).Because of interpolation effects these contiguousvelocity fields may be uncertain, especially nearthe edges. Any quantitative interpretation comesfrom the sparse velocity maps, which are not in-terpolated.

The Fabry-Perot data were wavelength andphase calibrated, with sky and continuum emis-sion subtraction performed, as described in detailin Knapen et al. (2000). The resulting reduceddata cubes were used to produce Hα velocity fieldmaps using gipsy, and following the prescriptionsgiven by Knapen (1997) and Knapen et al. (2000).The resulting velocity fields are shown in Figure 2.

4. Analysis

4.1. Rotation Curves

Rotation curves are powerful tools for revealingintrinsic kinematic characteristics of galaxies, in-cluding those of the nuclear rings they may host.In our sample, the range in radius spanned bythe rotation curves is small when compared to theoverall disk size, but this is a result of the smallfield of view of the instrument and of the sensitiv-ity limit.

For each galaxy we derived the rotation curve(Figure 3) by fitting tilted rings to the sparsevelocity field through an iterative process (seeBegeman (1989) for procedural details). We chosethe incremental radius for each concentric ring tobe 1.5 arcsec, which is approximately half of thewidth of a given fiber. We supplied the initialinput values for the nuclear ring center, inclina-tion, and position angle, as measured from I-bandimages (M08). We derived the initial center posi-tion by taking the point where the I-band emissionis the highest near the galaxy center. The inputvalue for vsys in the fit to the velocity field is from

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Fig. 1.— Results from the DensePak sample. From left to right, I band image from M08 with velocity fieldoverlaid in contours, residual velocity field with contours, and Hα emission image from M08. The center ofthe galaxy is indicated with a cross in each panel. Contour levels in the left panel are spaced by 5 km s−1

with dotted contours representing velocities less than the systemic velocity and solid contours representingthose velocities greater than the systemic velocity. Residual velocity contours and grayscales within the ringsgenerally range from −10 to 10 kms−1 except for NGC 1530 whose contours range from −20 to 20 km s−1,and NGC 473 and NGC 7742 which both have residual ranges from −5 to 5 km s−1. N is up, E to the left.The size of the field shown is 10 arcesc (RA) by 40arcsec (DEC) for all galaxies.

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Fig. 1.— continued.

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Fig. 1.— continued.

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Fig. 2.— As Fig.1, now for the three galaxies observed with the TAURUS Fabry-Perot instrument. Panelsare, from left to right, velocity field (grayscale and contours), result after subtracting a model velocity fieldbased on the rotation curve from the observed velocity field, and Hα integrated intensity. The center ofthe galaxy is indicated with a cross. The field of view shown is 15, 35, and 15 arcsec square for NGC 1300,NGC 4321, and NGC 6951, respectively. Contour levels for the first (leftmost) panel are for NGC 1300 from1472 to 1552km s−1 (white contours) and from 1572 to 1672km s−1 (black); for NGC 4321 from 1480 to1560 (white) and from 1580 to 1680km s−1; and for NGC 6951 from 1300 to 1440 (white) and from 1460to 1600km s−1—all contours are spaced by 20 km s−1 and the grayscale range is the same as that spannedby the contours. In panel 2, contour levels for all galaxies are from −45 to 0 km s−1 (white) and from 15 to45 km s−1 in steps of 15 km s−1; the grayscale range is from −50 to 50 km s−1 for NGC 1300 and NGC 6951but from −30 to 30 kms−1 for NGC 4321. For all three galaxies, the grayscale in panel 3 indicates the rangeof values in instrumental units.

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the NASA/IPAC extragalactic database (NED).One exception is NGC 5953, whose systemic veloc-ity was derived from the data due to a 26 km s−1

difference with the NED value. For the initial run,although we supplied input values, all parameterswere left free. We first determined the center posi-tion and then fixed only that value for the seconditeration to then determine the systemic velocity.Once the center and systemic velocity were fixedwe determined the inclination and position angle(third and fourth iterations, respectively). Withthe four values then fixed, we fit the rotationalvelocity. We gave more weight to positions alongthe major axis, since those data points carry mostof the information about rotational velocities. Inmost cases we used the inclination of the outer diskfor the final fit. However, in the cases of low incli-nation (below 25), we adopted the photometricorientation parameters from M08 as initial inputsto the routine since the fitting routine producedinclinations with high uncertainties. Even withsuch low inclinations the position angle was deter-mined accurately with a tilted ring fit. Becauseour data sets span a small range in radius, it wasnot feasible to make sophisticated fits to the ve-locity fields.

The uncertainties on the velocities derived fromthe line fits range from 0.5kms−1 to 5km s−1. Anadditional source of uncertainty is due to the un-known location of the Halpha emission within thearea seen by each fiber. The amplitude of this un-certainty depends on the velocity gradient acrossthe face of the fiber. We estimated this gradientfor all fibers using the derived rotation curves, andfound that a value of 8 km s−1 is representative ofa 1σ uncertainty.

Rotation curves for the Fabry-Perot data weresimilarly generated, but here, the smaller pixel sizeand full spatial sampling allowed us to fit the ro-tation curves with radial steps of 0.5 arcsec fromthe center outward.

4.2. Residual Velocity Fields

We constructed residual velocity maps (Fig-ure 1, panel 2) for the velocity fields (both thesparse and interpolated versions for the DensePakdata) by subtracting a smooth model velocityfield, constructed from the rotation curve and theassumed orientation parameters. As with the in-terpolated velocity fields, the interpolated residual

maps should only be used for general impressions.These maps, however, are useful because they givea better sense of patterns in the image.

4.2.1. Within the rings

We find that all of the nuclear rings in our sam-ple have low residual velocities (both approachingand receding) near the central ridge of the ring(ranging from ∼5 kms−1 to ∼20 kms−1). The nu-clear rings in NGC 473 and NGC 7742 are notresolved enough to comment on here, as the asso-ciated residuals do not overcome the uncertaintiesassociated with the measured velocity, wavelengthcalibration, and position of the Hα peak within agiven fiber beam. Patches of approaching and re-ceding residual velocity peaks of ∼10kms−1 occurin the nuclear rings of NGC 1343, NGC 4314, andNGC 5953, and reach to near 20 km s−1 in therings of NGC 1530 and NGC 5248. Since thesevalues are close to the combined measurement un-certainty, they can provide no firm evidence forthe existence and origins of non-circular motions(in NGC 4321 the situation is better, as discussedin detail by Knapen et al. 2000).

A comparison of the kinematic and photometriccenters of the sample reveals no strong asymme-tries. The degree to which the centers differ is pro-portional to the lopsidedness of the potential, andthus a good indicator of the amount of non-circularmotion (Franx et al. 1994). After computing thedifference between the kinematic and photometriccenter positions (see Table 2), we see that the cen-ter positions agree to within the uncertainties ofthe photometric center measurements. This agree-ment, in combination with the small noncircularmotions, suggests the nuclear rings are circular innature.

4.2.2. In the vicinity of the rings

For some of the galaxies in our sample, our ob-servations cover part of the velocity field outside ofthe nuclear ring as well. This allows us to studythe interaction between the bar and the nuclearring in those cases.

Sufficient, albeit limited, Hα radial coverage al-lows us to comment on the velocities of the barredgalaxies near the outer edge of the nuclear ring,perpendicular and parallel to the bar major axis.In all cases, we can see the influence of the strong

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Fig. 3.— Rotation curves with the radial range (i.e., width) of the nuclear rings shadowed. The turnoverradius is denoted by the dashed vertical line. See Table 3 for ring widths.

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Table 2: Kinematic parameters for the observed sample

NGC Vsys Offset φkin | φkin − φphot | | φd − φkin | | Ctrkin − Ctrphot |x y x y

(km s−1) (′′) (′′) () () () (′′) (′′)(1) (2) (3) (4) (5) (6) (7)473 2135 −5.0 +7.5 156 2 3 0.6 0.31300 505 n/a n/a 80 55 26 n/a n/a1343 2215 −5.3 +6.5 7 53 73 0.9 1.31530 2450 −1.6 +11.0 5 20 3 0 0.32903 560 −4.0 +7.4 5 3 12 2.8 0.93351 764 −4.2 +7.0 30 10 17 0 0.94303 1560 −3.4 + 7.5 117 29 − 0.1 04314 979 −4.0 +5.5 122 13 − 1.0 0.84321 1578 n/a n/a 150 20 120 n/a n/a5248 1149 −2.9 +6.3 115 0 5 0.4 0.25953 1991 −6.0 +6.7 49 57 120 0 0.16951 1423 n/a n/a 136 10 106 n/a n/a7742 1658 +0.7 +6.6 131 2 − 0 0.9

Notes: NGC numbers of the target galaxies are listed in order of increasing RA (col. 1). Systemic velocity(col. 2), nuclear ring kinematic center position with respect to the center of the DensePak array (col. 3)and kinematic position angle (col. 4) were derived using the gipsy rotcur task. Typical uncertainties forVsys are ±8 km s−1, center position ±0.09 arcsec, and position angle ±5. The difference (absolute value)between the kinematic and photometric position angles (see Table 1) is in col. 5, with the difference betweenkinematic and disk position angles in col. 6. The difference between kinematic and photometric centers is incol. 7.

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bars as they create high residual velocities. How-ever, once they interact with the nuclear ring outerboundary, residual velocities sharply decrease andplateau within the nuclear rings. For NGC 4314,we see ordered velocity patterns increasing nearthe outer edge of the ring (both approaching andreceding) close to both sides of the bar minor axis,where the bar dust lanes merge with the ring.Residuals approach 60 kms−1 in both directions,with a strong velocity transition zone near theouter boundary of the nuclear ring, where valuesreach 90 kms−1 (approaching) at the edge of theFOV. Although the spatial sampling is poor at theimage edge, our observations do agree with veloc-ity values from Benedict et al. (1996).

The residuals for NGC 5248 near the westernside of the bar minor axis reach 40 km s−1, with aweaker-defined, although evident, transition zoneas radii approach the outer ring boundary. Theseresults are consistent with the two-dimensionalCO velocity field presented by Jogee et al. (2002).In both galaxies, good agreement with the litera-ture adds confidence that the results we see at thefield edges are not artificial, even though our dataare spatially sparse.

The residual map of NGC 1530 provides us withthe clearest picture of the interaction between thebar and the ring. In Fig. 4 we see large velocityexcesses (∼110 km s−1) to the west of the nuclearring, near its exterior edge. The high residuals areassociated with the large scale bar. The strongresiduals sharply decrease to 50kms−1 over a smalltransition zone near the outer boundary of thenuclear ring. Although we see no obvious resid-ual patterns near the bar major or minor axes ofthe nuclear ring, we note that the largest residualvelocities (∼120 kms−1) across our sample occurin this galaxy, between the bar major and minoraxes, on the west side just exterior to the ringouter boundary. A closer look in the vicinity radi-ally shows a very sharp transition at the locationof the nuclear ring, where residual velocities dropto 10 kms−1. Zurita et al. (2004) observe a nearlyidentical pattern in the corresponding Hα map ofthe circumnuclear environment.

The TAURUS data of NGC 4321 used here wereanalyzed and discussed in detail by Knapen et al.(2000). In the residual velocity map, they high-lighted the contributions from the inner part ofthe bar and the spiral arm fragment coming into

Fig. 4.— Velocity curve for NGC 1530 at radiiwithin (top plot) and exterior to (bottom plot)the nuclear ring. The radial coverage within thenuclear ring is further divided to show velocitiesalong the inner and outer halves of the ring. Out-side of the nuclear ring, velocities from the nu-cleus to the ring inner edge are plotted, as wellas those from the ring outer edge to the radiallimits of the FOV. The velocity is plotted with re-spect to the systemic velocity, normalized by therotation velocity, and adjusted by removing theinclination in order to allow comparison with thecurve representing circular motion. The bar ma-jor axis (solid lines) and minor axis (dotted lines)are drawn for context. Note that there is a phaseshift of 90, plus the difference between the kine-matic position angle of the velocity data pointsand the photometric position angle used to cre-ate the model curve, to allow the cross-over pointto occur at 180. The area azimuthally located between the bar major and minor axes shows thelargest velocities of the sample, with deviationsreaching 110 km s−1.

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the nuclear (pseudo-)ring from the main part ofthe bar. These result in a broadly symmetric pat-tern of positive and negative residual velocities,mapping out the non-circular motions due to barand spiral streaming motions.

5. Results

5.1. Circular Nuclear Rings

For most of the sample, we find that the nuclearrings are nearly circular and in the same plane asthe disk. The shape and orientation with respectto the host disk were deduced by comparing theposition angle (of the nuclear ring, φr and disk,φd) combined with the ellipticity of each nuclearring, ǫr to that of its host disk, ǫd. We used thephotometric position angles and ellipticities of thenuclear rings from M08. The kinematic positionangles of the nuclear rings were extracted fromthe rotation curve generation. In Figure 5, wecompare the various position angles and see thatin most cases the photometric and kinematic po-sition angles are similar. The same can be saidfor both the photometric and kinematic positionangles with respect to the galactic disk positionangle. This finding, coupled with the result fromM08 of a similar relationship with respect to thedisk and nuclear ring ellipticities (fourth panel),corroborate s our idea that nuclear rings are cir-cular and oriented as their host disk.

We note three cases that are significantly abovethe scatter and thus do not meet our criteriaof a round in-plane nuclear ring: NGC 1300,NGC 1343, and NGC 5953. The ring in NGC 1300is not fully sampled azimuthally (see Figure 2),which adds a high level of uncertainty for the pho-tometric position angle and ellipticity. NGC 5953is nearly face on and morphologically patchy andround along the line of sight, a combination thatcreates high position angle uncertainty.

The residual maps (Fig. 1 and Fig. 2, panel 2)also indicate that within the uncertainties ofour observations (see Section 4.1), the nuclearrings are circular. There may be noncircu-larites at a lower level which may be relatedto the local underlying potential (as noted forNGC 4321 - Knapen et al. (1995); NGC 1068 -Schinnerer et al. (2000); and NGC 5383 - Duval(1977); Sheth et al. (2000)).

, ,

NGC 473 NGC 2903 NGC 4321

NGC 1300 NGC 3351 NGC 5248

NGC 1343 NGC 4303 NGC 5953

NGC 1530 NGC 4314 NGC 6951

NGC 7742

Fig. 5.— Comparisons for ring kinematic vs. ringphotometric (top), ring photometric vs. disk pho-tometric (middle), and ring kinematic vs. diskphotometric (bottom) position angles. Ellipticitycomparison of the ring and disk is also plotted.The disk position angle is not given in the RC3 forNGC 4303, NGC 4314 and NGC 7742. The meanerror on the disk position angle is unknown, butthe error increases as the ratio of isophotal majorto minor axes decreases (logR25). We assigned a5 error for the smallest ratio in the sample andproportionally computed the other errors. Errorsare smaller than the size of the graphic icons ofeach galaxy.

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Table 3: Nuclear ring and bar properties.

NGC Nuclear RelRing Ring Qg Compactness Rt DiskActivity Size Width sma

(kpc) (104 (km s−1)2 kpc−1) (kpc) (kpc)(1) (2) (3) (4) (5) (6) (7) (8)473 − 0.20 0.62 0.12 1.1 1.4 7.41300 − 0.02 0.13 0.54 16.5 0.31 18.21343 − 0.11 0.31 0.15 2.3 0.3 11.11530 − 0.05 0.62 0.73 8.2 1.4 24.52903 H ii 0.08 0.01 0.27 11.7 0.1 16.33351 H ii 0.04 0.09 0.22 36.1 0.2 4.94303 H ii 0.01 0.20 0.28 23.8 .2 14.44314 LINER 2 0.05 0.11 0.43 8.6 0.3 5.94321 Transition 2 0.04 0.38 0.22 15.8 0.2 21.75248 H ii 0.03 0.49 0.10 4.6 0.5 20.55953 LINER 2, Sy2 0.13 0.90 0.1 9.8 0.35 7.76951 Sy 2 0.03 0.23 0.28 9.9 0.25 13.87742 Transition 2 0.18 0.63 0.06 5.8 0.32 5.5

Notes: Identification (col. 1); presence and type of nuclear activity (col. 2, from Ho et al. 1997b when available,

NGC 1530 and NGC 5953 are from NED); relative nuclear ring size (col. 3) defined as ring semi-major axis (see

Table 1, col 11) divided by disk semi-major axis (half of the host major disk diameter), D0 from NED (col 9); ring

width (col. 4) defined as the difference between the isophotal inner ring boundary and outer ring boundary, divided

by the disk semi-major axis; non-axisymmetric torque parameter (col. 5), from Comeron et al. 2009; when no Qb

value exists, we adopt a known Qg value instead: NGC 1530 (Block et al. 2004) and NGC 5953 (H. Salo, private

communication); rotation curve compactness (col. 6); rotation curve turnover radius (col. 7); We estimate that on

average the uncertainty in the compactness is ≈75km s−1kpc. Uncertainties in the various size measurements involved

were also added in quadrature to yield typical uncertainties in the relative ring size and width of ±0.01. Uncertainties

associated with the non-axisymmetric torque parameter, Qg, were adopted from Comeron et al. (2009) to be ±0.1.

NGC 473

NGC 1300

NGC 1343

NGC 1530

NGC 2903

NGC 3351

NGC 4303

NGC 4314

NGC 4321

NGC 5248

NGC 5953

NGC 6951

NGC 7742

Fig. 6.— Left panel: Radial location of the nuclear rings versus the rotation curve turnover radius. Thelocations generally coincide within the uncertainties. The spread is most likely due to the higher uncertaintyassociated with the ridge location (radial ring center) of the wider rings NGC 1343, NGC 4321, NGC 5953,and NGC 7742. Right panel: Ring width versus relative ring size. As the relative ring size increases so doesthe ring width.

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NGC 473 NGC 2903 NGC 4321

NGC 1300 NGC 3351 NGC 5248

NGC 1343 NGC 4303 NGC 5953

NGC 1530 NGC 4314 NGC 6951

NGC 7742

Fig. 7.— Rotation curve compactness versus relative nuclear ring size (panel 1), nuclear ring width (panel 2),and the non-axisymmetric torque parameter Qg (panel 3). Panel 4 shows the relative ring size as a functionof Qg. Typical error bars (refer to Table 3 caption) are within the size of the icons.

5.2. Mass Concentration and Nuclear

Ring Size

An indication of the central mass concentra-tion can be obtained from the compactness, e.g.,de Blok et al. (1996). We define compactness asV 2/Rt, where V is the rotational velocity differ-ence between the radial location of the turnoverradius, Rt, and the origin (0,0). The turnover ra-dius is defined as the point in the rotation curvehalfway between the initial steeply rising compo-nent and the flat(ter) segment. For the few galax-ies with very steeply rising rotation curves, suchas NGC 2903 and NGC 3351, the turnover ra-dius cannot be measured accurately, and hence thecompactness is uncertain. In these cases, the com-pactness should be considered a lower limit.

Table 3 lists the compactness and turnover lo-cations. As expected, the compactness decreaseswith increasing turnover radius (not shown graph-ically, but the values are in the Table. In lineartheory, which is not strictly applicable here butyields useful approximations, the turnover radiusin the rotation curve sets the location of the ILRs,and they in turn determine where inflowing gaspiles up, which ultimately forms the nuclear ring(Knapen et al. 1995; Buta & Combes 1996). In-deed, the location of the nuclear rings correlateswell with the turnover radius (see Figure 3 and theleft panel of Figure 6), which we can identify with

the phenomenon identified above.

In panel 1 of Fig. 7 we compare the relativering size, that is the nuclear ring semi-major axisdivided by the semi-major axis of the host galaxy,to the compactness parameter as derived from therotation curve. We find that the relative ring sizeincreases as the compactness decreases.

The relative ring size is compared to the non-axisymmetric galactic torque, Qg, in panel four ofFig. 7. This torque parameter, originally definedby Combes & Sanders (1981) to characterize barstrength, quantifies the overall influence of galacticnon-axisymmetries. Specifically, Qg is the maxi-mum tangential force at a given radius divided bythe radial force. For all galaxies except two, weadopt the Qg values from Comeron et al. (2010),as noted in Table 3, since they applied a consistentcomputation method for all of the nuclear ringsseen in our sample. We confirm (Fig. 7) that thehighest torque values occur in those galaxies withthe smaller rings relative to the size of their hostdisk (Knapen 2005; Comeron et al. 2010). As thetorque weakens below Qg = 0.4 any size ring canform, but higher torque values (”stronger bars”)progressively limit the nuclear ring size.

The compactness and the non-axisymmetrictorque Qg do not correlate (panel 3 of Fig. 7).Also, the turnover and Qg do not correlate (notshown graphically). This may be because the non-

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axisymmetric torque is a parameter driven moreby the azimuthal than the radial distribution ofmass, whereas the opposite is the case for theturnover radius and compactness.

5.3. Nuclear Ring Width Comparisons

The width of a nuclear ring is an important pa-rameter because it very much defines how well aring is visible in an Hα image, and how it is seenin contrast with the background emission from thehost galaxy. Using the ring parameters we havenow determined, it is interesting to see whetherthe ring width is driven by the physical propertiesof the host galaxy. So, as a first step, we define thering width as the difference between the inner andouter ring boundaries, as defined from the emis-sion in Hα, and then plot the width of the nuclearring against the relative ring size (right panel ofFig. 6). We see a trend that larger nuclear ringsare wider, which might not have been expected apriori.

We then compare the compactness to the nu-clear ring radial width (panel 2 of Fig. 7). Thereis some evidence for a trend of compactness withring width, where a nuclear ring is wider as thecompactness decreases. We can thus conclude thatincreased compactness leads to both smaller andnarrower nuclear rings, which is in accord with theexpectations from linear theory and the locationof a pair of ILRs near the turnover radius of arotation curve. This clear link between the kine-matics of the galaxy and the morphological pa-rameters of the nuclear rings is thus further directevidence for a resonant origin of the nuclear rings,deeply linked to the underlying structure of thehost galaxy. This evidence based on kinematicssupplements earlier evidence based almost exclu-sively on morphology, as reviewed and extendedby Comeron et al. (2010).

6. Concluding Remarks

We combined DensePak integral field unit andTAURUS Fabry-Perot observations for a sample of13 galaxies that contain nuclear rings. Based onthis sample, we note the following new findings:

• Nuclear rings are intrinsically circular andunaffected by the local non-axisymmetric en-vironment that can exist from active star for-

mation within the rings; they are influencedby global phenomenon that can affect thepotential, such as a bar.

• The compactness, derived from the rotationcurves, decreases as the ring width increases.

• The compactness also decreases as the rela-tive ring size increases

• As the relative nuclear ring size increases sodoes the width of the ring

• Strong bars with a Qb of 0.4 or greater canonly be accompanied by small and thin nu-clear rings. For smaller torques, the ring sizecan vary.

We have also reaffirmed several standing find-ings:

• True to resonance theory, the location ofthe nuclear rings correlates well with theturnover radius.

• The highest torque values occur in thosegalaxies with the smaller rings relative to thesize of their host disk.

In those cases with sufficient radial coverage,we agree that

• For NGC 4314 residual velocities sharply de-crease and plateau within the nuclear rings.Ordered velocity patterns increase near theouter edge of the ring (both approaching andreceding) close to both sides of the bar minoraxis.

• The residual velocities for NGC 5248 nearthe western side of the bar minor axis reach40 km s−1, with a weaker-defined, althoughevident, transition zone as radii approachthe outer ring boundary.

• In the case of NGC 1530 large velocity ex-cesses exist to the west of the nuclear ring,near its exterior edge and then sharply de-crease over a small transition zone near theouter boundary of the nuclear ring.

The Fabry-Perot observations were made withthe William Herschel Telescope operated on the

17

island of La Palma by the Newton Group of Tele-scopes in the Spanish Observatorio del Roque delos Muchachos of the Instituto de Astrofısica deCanarias.

The Integral Field Unit observations were madewith the WIYN Observatory which is owned andoperated by the WIYN Consortium, consisting ofthe University of Wisconsin, Indiana University,Yale University, and the National Optical Astron-omy Observatory (NOAO). The WIYN is part ofthe Kitt Peak National Observatory located inTucson Arizona.

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